I need a break. Should I ask her to take Mom at least for the day so I can have time to myself?

How does your mom get along while you work? What are her care needs? What is/are her impairments? Mobility issues? Vision problems? Respiratory disease? Cancer? Dementia? Knowing these things will be helpful to our answers.

About your sister: Sure, ask her if she can invite Mom over for a full day. Just don't be surprised or disappointed if she says No (with a lot of excuses, of course).

Acknowledge that caring for your mother was your decision, and it still is your decision. It sounds like you bit off more than you can chew (a VERY common scenario) and you need to reassess what you can realistically do alone (or with the minimal help your sister is willing to provide).

It seems to me the first thing to address is being able to sleep through the night. Why isn't Mom quietly in bed when you are?

When you are getting a good night's sleep most nights it is much easier to keep daytime situations in perspective. Sleep deprivation is used as a torture technique after all -- it is very disruptive to normal functioning. So first and foremost solve that.

If Mom can be safely on her own at night, then your need is to muffle the noise she makes. Put felt furniture pads on the walker legs. Wear ear plugs. Use white noise or soft music to distract you.

But if Mom has safety issues when she is up during the night and you can't safely just muffle the noise, then if she is having insomnia or other sleep issues, talk to her doctor about that. Make it clear that this is not a trivial issue, and that you being able to keep mom at home depends on solving the sleep issues.

I think the sleep issue comes first. Then you can consider other aspects of your decision to care for Mom. It doesn't have to be all or nothing. She could live with you but go to an adult day care center. You could have help come in several days a week. Definitely hire household help like cleaners and yard work, if applicable. It doesn't have to be all on your shoulders. (And in this regard consider yourself an only child.) Even if you ultimately decide that Mom needs a care center, that doesn't mean you give up all caregiving responsibility.

But first, solve the sleep problem.

Look for a local day-care program for seniors. MY Mom goes to one on fridays. It is available all the time...but, Friday is her "special" day. (And my only full day for myself).

Is there a non-profit adult day care in your area? They are often very reasonable for the services they provide. Also try searching "respite coalitions." We just got a small grant from a respite group to pay for someone to help. Your Area Agency on Ageing might have information on services.
Unfortunately, in my experience, once the siblings get another sibling in the position of being the caregiver they make themselves scarce.

Annabelle, the start of caregiving is often the worst for new caregivers. They feel they have to do everything perfectly on their own. Can you assess the financial aspects of your Mom's care and determine how you can bring in other helpers to reduce your stress and day to day care needs? Is this a permanent situation? Then Mom should be contributing. And if you see Medicaid as a possibility in the future, then you need a care contract to justify the outlay of Mom's money . You can shop on the internet for just about EVERYTHING and reduce those shopping trips. You can find a laundry that you can drop off (or some even pick up) and the laundry is washed, dried and folded. Get some houskeeping help - it's nice to come home to a clean house - that someone else cleaned. Is your Mom capable of helping - even with small things?
If you can tell us more about your Mom's needs, her age, etc others may have even more ideas.

How was it agreed upon that your mother would move in with you, and that you would be responsible for her caregiving?

Annabelle, what are your mother's care needs? She's come to live with you, has she, in your house? Are you on your own with her or do you have a family as well as your job?

Sisters shmisters. It's actually much more important to figure out how you're going to make your plan workable without other family members so that it doesn't particularly bother you if she doesn't contribute - and don't despair, there will be a way.

I am sympathetic to your frustration. However - these are my words of advice:

You can't make a sibling who doesn't want to help - help.

You can't make a sibling care, when they don't.

However you ended up as your mothers caregiver- unless it was contingent upon and agreed upon that sister would help - this is the choice you made - even if it felt as if you really had no other choice.

Absolutely- it would be great if your sister would help out more - it's the right thing to do, afterall. BUT - this brings us full circle to - you can't make anyone help, who really doesn't want to.

So - now you're angry, frustrated and bitter over something that is likely not going to change - so quit hoping and thinking that it will. It won't.  Honestly- the sooner you accept that, the better off you'll be.